Signature Placement in Post-Quantum TLS Certificate Hierarchies: An Experimental Study of ML-DSA and SLH-DSA in TLS 1.3 Authentication

Abstract: Post-quantum migration in TLS 1.3 should not be understood as a flat substitution problem in which one signature algorithm is replaced by another and deployment cost is inferred directly from primitive-level benchmarks. In certificate-based authentication, the practical effect of a signature family depends on where it appears in the certification hierarchy, how much of that hierarchy is exposed during the handshake, and how cryptographic burden is distributed across client and server roles. This paper presents a local experimental study of TLS 1.3 authentication strategies built on OpenSSL 3 and oqsprovider. Using a reproducible laboratory, it compares ML-DSA and SLH-DSA across multiple certificate placements, hierarchy depths, and key-exchange modes, including classical, hybrid, and pure post-quantum configurations. The clearest discontinuity appears when SLH-DSA is placed in the server leaf certificate. In that configuration, handshake latency and server-side compute cost increase by orders of magnitude, while strategies that confine SLH-DSA to upper trust layers and preserve ML-DSA in the interactive leaf remain within a substantially more plausible operational range. The results further show that transport size alone does not explain the heavy regime: once SLH-DSA reaches the leaf, server-side cryptographic cost becomes dominant. The paper argues that post-quantum TLS migration is best evaluated as a problem of certificate-hierarchy design, chain exposure, and cryptographic cost concentration during live authentication.